The Everyday Math HELIX

Content Strands	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5
Numeration	Make progress in oral counts, reading numbers and writing numbers.	Reading and writing numbers; investigating place-value of whole numbers; exploring fractions and money.	Counting; reading and writing numbers; identifying place-value; comparing numbers; working with fractions; using money to develop place-value and decimal concepts.	Counting patterns; place-value; reading and writing whole numbers through 1,000,000; fractions, decimals, and integers.	Reading, writing, and comparing whole numbers through millions, decimals through thousandths, negative numbers to –20, and fractions; understanding relations between fractions, decimals, and percents; locating fractions and mixed numbers on a number line; generating equivalent fractions.	Reading, writing, and comparing negative numbers, fractions, whole numbers through billions, and decimals through thousandths; reading, writing, and interpreting whole-number powers of 10; translating between exponential and standard notation; understanding and identifying prime numbers, composite numbers, and square numbers.
Operations and Computation	Solve concrete problems that arise from children’s daily life in the classroom.	Learning addition and subtraction facts, fact families, and extended facts; beginning informal work with properties of numbers and problem solving.	Recalling addition and subtraction facts; exploring fact families; adding and subtracting with tens and amounts.	Multiplication and division facts extended to multi-digit problems; working with properties; operations with fractions and money.	Using paper-and-pencil algorithms to add, subtract, multiply, and divide multi-digit whole numbers and decimals; using mental arithmetic to compute exact answers and to estimate; rounding from millions to hundredths; modeling multiplication with arrays and area; doing operations with fractions.	Using paper-and-pencil algorithms to add, subtract, multiply, and divide multi-digit whole numbers and decimals; using mental arithmetic to compute exact answers and to estimate; rounding from billions to hundredths; translating among fractions, decimals, and percents; prime factoring; converting between fractions and mixed numbers; adding and subtracting fractions and mixed numbers with unlike denominators, finding least common multiples and greatest common factors; multiplying and dividing fractions.
Measurement and Reference Frames	Using games, activities and everyday activities to explore the concepts of telling time and measuring time duration; beginning understanding of toes of measure.	Using tools to measure length, capacity, and weight; using clocks, calendars, timelines, thermometers, and original numbers.	Using tools to measure length, capacity, weight, and volume; using U.S. customary and metric measurement units.	Recording equivalent units of length; recognizing appropriate units of measure for various items; finding the areas of rectangles; using multiplication arrays, coordinate grids, thermometers, and map scales to estimate distances.	Using tools to measure length area, volume, weight, temperature, and time; developing personal references for inches, centimeters, feet, meters, and yards; estimating lengths and weights; finding areas and perimeters of rectangles, parallelograms, and triangles; finding volumes of rectangular prisms by counting cubic units; calculating elapsed time; using correct units in all measurements; calculating distances using map scales.	Measuring and estimating length, area, volume, weight, and capacity; converting and computing with common units of measure; creating scale drawings.

Content Strands	Kindergarten	Grade 1	Grade 2	Grade 3	Grade 4	Grade 5
Data and Chance	Gathering information, displaying it, discussing it and explaining the results and making count comparisons.	Collecting, organizing and displaying data using tables, charts, and graphs; exploring concepts of chance.	Collecting, organizing and interpreting data using tables, charts, and graphs; exploring concepts of chance.	Creating, reading, and interpreting graphs; identifying landmarks in data sets, including range, median, mode, and mean; listing all possible outcomes in simple situations; using fractions to quantify probabilities; using experimental results to make predictions.	Data and Chance Creating, reading, and interpreting graphs; identifying landmarks in data sets, including range, median, mode, and mean; listing all possible outcomes in simple situations; using fractions to quantify probabilities; using experimental results to make predictions.	Comparing probabilities for different outcomes; comparing theoretical and experimental probabilities; expressing probabilities as fractions, decimals, and percents; drawing justifiable conclusions from data; displaying data in more than one way; formulating a question, carrying out a survey or experiment, recording data, and communicating results; drawing and interpreting circle graphs and stem and leaf plots; understanding measures of central tendency (mean, me mode).
Geometry	Varied experiences with 2- and 3-dimensional shapes.	Exploring 2- and 3-dimensional shapes.	Exploring 2- and 3-dimensional shapes; classifying polygons.	Exploring 2- and 3-dimensional shapes and other geometric concepts.	Geometry Locating points on a coordinate grid; drawing and measuring angles; classifying angles as acute, obtuse, or right; classifying lines as parallel, intersecting, or perpendicular; recognizing and using transformations, including reflections and rotations; understanding the relationship between reflections and line symmetry; building 3-dimensional shapes; describing, comparing, and analyzing 2-dimensional and 3-dimensional figures.	Geometry Constructing a circle with a given radius or diameter; defining and creating tessellations; measuring and drawing angles, including reflex and straight angles; identifying and defining right, isosceles, and equilateral triangles; plotting points in four quadrants; using translations, reflections, and rotations; solving perimeter, area, and volume problems; understanding the relationship between the volumes of cones/pyramids and cylinders/prisms; finding the surface area of a cube and the area of a circle; identifying angle relationships in triangles and in quadrilaterals.
Patterns Functions and Algebra	Beginning to explore attributes, patterns, sequences, relations and functions; introduction to “What’s My Rule?” problems.	Exploring attributes, patterns, sequences, relations, and functions; finding missing numbers and rules in Frames-and-Arrows and “What’s My Rule?” problems; studying properties of operations.	Exploring number patterns, rules for number sequences, relations between numbers, and attributes.	Finding patterns on the number grid; solving Frames-and-Arrows puzzle having two rules; completing variations of “What’s My Rule?” activities; exploring the relationship between multiplication and division; using parentheses in writing number models; naming missing parts of number models.	Using letters and other symbols for unknowns; simplifying expressions containing parentheses; creating, extending, and describing patterns; using formulas for finding the area of simple geometric figures; determining rules that relate numbers in pairs; finding missing numbers in tables; translating among verbal, numerical, and graphical representations; understanding and writing number models for number stories.	Patterns, Functions, and Algebra Evaluating simple algebraic expressions; finding rules for patterns; finding the nth term in a sequence; solving simple open number sentences and simple rate problems; working with equations by doing the same thing to both sides; understanding simple direct proportion; using variables and equations to represent situations; graphing ordered pairs; translating among verbal, numerical, and graphical representations.